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Dive into the research topics where R. de la Rosa is active.

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Featured researches published by R. de la Rosa.


Applied Mathematics and Computation | 2016

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

R. de la Rosa; M. L. Gandarias; M. S. Bruzón

In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does not require the use of a variational principle. We also construct conservation laws by using Ibragimov theorem which is based on the concept of adjoint equation for nonlinear differential equations.


Journal of Mathematical Chemistry | 2015

A study for the microwave heating of some chemical reactions through Lie symmetries and conservation laws

R. de la Rosa; M. L. Gandarias; M. S. Bruzón

In this paper, we consider an equation describing microwave heating and we find the subclasses of equations which are nonlinearly self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for this equation.


Archive | 2014

Conservation Laws of a Family of Reaction-Diffusion-Convection Equations

M. S. Bruzón; M. L. Gandarias; R. de la Rosa

Ibragimov introduced the concept of nonlinear self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi-self-adjoint equations. Gandarias defined the concept of weak self-adjoint. In this paper, we found a class of nonlinear self-adjoint nonlinear reaction-diffusion-convection equations which are neither self-adjoint nor quasi-self-adjoint nor weak self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for these equations.


Archive | 2019

An Overview of the Generalized Gardner Equation: Symmetry Groups and Conservation Laws

M. S. Bruzón; M. L. Gandarias; R. de la Rosa

In this paper we study the generalized variable-coefficient Gardner equations of the form u t + A(t)f(u)u x + C(t)f(u)2u x + B(t)u xxx + Q(t)F(u) = 0. This family of equations includes many equations considered in the literature. Some conservation laws are derived by applying the multipliers method. The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. We study the equation from the point of view of Lie symmetries in partial differential equations. Finally, we calculate exact travelling wave solutions of the equation by using the simplest equation method.


Applied Mathematics and Computation | 2018

Exact solutions via equivalence transformations of variable-coefficient fifth-order KdV equations

M. S. Bruzón; R. de la Rosa; Rita Tracinà

Abstract In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are obtained. Invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations. Here, differential invariants are applied to obtain exact solutions.


Archive | 2016

Travelling Wave Solutions of a Generalized Variable-Coefficient Gardner Equation

R. de la Rosa; M. S. Bruzón

In this paper, a simple way to construct exact solutions by using equivalence transformations is shown. We consider a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We obtain the continuous equivalence transformations of the equation in order to reduce the number of arbitrary functions and give a clearer formulation of the results. Furthermore, we calculate Lie symmetries of the reduced equation. Then, we determine the similarity variables and the similarity solutions which allow us to reduce our equation into an ordinary differential equation. Finally, we obtain some exact travelling wave solutions of the equation by using the simplest equation method.


Journal of Computational and Theoretical Transport | 2016

Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

R. de la Rosa; M. L. Gandarias; M. S. Bruzón

ABSTRACT Symmetry group analysis is carried out on a generalized fifth-order KdV (foKdV) equation involving many arbitrary functions. Equivalence transformations group has been determined. This allows us to perform a comprehensive study by reducing the equation to a subclass with fewer number of arbitrary elements. Furthermore, we have established the subclasses of the reduced equation which are nonlinearly self-adjoint. The property of nonlinearly self-adjointness is used to construct conserved vectors from the classical symmetries of the equation by using a general theorem on conservation laws. We also determine conservation laws by using the multipliers method.


Communications in Nonlinear Science and Numerical Simulation | 2016

Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation

R. de la Rosa; M. L. Gandarias; M. S. Bruzón


Chaos Solitons & Fractals | 2016

Conservation laws and exact solutions of a Generalized Benjamin–Bona–Mahony–Burgers equation

M. S. Bruzón; T. M. Garrido; R. de la Rosa


Nonlinear Dynamics | 2016

Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

R. de la Rosa; M. L. Gandarias; M. S. Bruzón

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